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Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = Fq +uFq + u²Fq, where u³ = 0 mod q. Further, we find a unique set of generators for cyclic codes over R and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over R is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results. [ABSTRACT FROM AUTHOR]

A QTAG-module M is an α-module, where α is a limit ordinal, if M/Hβ(M) is totally projective for every ordinal β < α. Here we show that totally projective mod- ules and α-modules of length α, where α has cofinality ω, are projectively socle-regular. We also show that a summable ω1-module need not be a direct sum of countably gen- erated modules, where ω1 is the first uncountable ordinal. [ABSTRACT FROM AUTHOR]